(-3+7i)(1-2i)

Jasonbradley

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Jun 16, 2024

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Multiplying Complex Numbers: A Step-by-Step Guide

This article will walk you through the process of multiplying two complex numbers: (-3 + 7i) and (1 - 2i).

Understanding Complex Numbers

Complex numbers are numbers that can be expressed in the form a + bi, where 'a' and 'b' are real numbers and 'i' is the imaginary unit, defined as the square root of -1.

Multiplication Process

To multiply complex numbers, we use the distributive property just like we do with real numbers.

1. Expand the expression: (-3 + 7i)(1 - 2i) = (-3)(1) + (-3)(-2i) + (7i)(1) + (7i)(-2i)

2. Simplify: = -3 + 6i + 7i - 14i²

3. Remember that i² = -1: = -3 + 6i + 7i - 14(-1)

4. Combine real and imaginary terms: = (-3 + 14) + (6 + 7)i

5. Final answer: = 11 + 13i

Conclusion

Therefore, the product of (-3 + 7i) and (1 - 2i) is 11 + 13i.

By following these steps, you can confidently multiply any two complex numbers.